Equipe:

Carlos Alberto Figueiredo - RM330568
Daiana Cristina Zanelli Mota - RM330722
Diogo Silva Rocha - RM330717
Renato Belandrino Rodrigues - RM330579

install.packages(“psych”) install.packages(“plotly”) install.packages(“gmodels”) install.packages(“corrgram”) install.packages(“lmtest”) install.packages(“rpart”) install.packages(“rpart.plot”) install.packages(“RandomForest”)

# mostrar atÈ 2 casas decimais
options("scipen" = 2)

# Ler arquivo csv


Vinhos <- read.csv2("BaseWineRedeWhite2018.csv", row.names=1)
#Vinhos <- BaseWine_Red_e_White2018
#fix(Vinhos)
#mostrar as vari·veis
str(Vinhos)
## 'data.frame':    6497 obs. of  13 variables:
##  $ fixedacidity      : num  6.6 6.7 10.6 5.4 6.7 6.8 6.6 7.2 5.1 6.2 ...
##  $ volatileacidity   : num  0.24 0.34 0.31 0.18 0.3 0.5 0.61 0.66 0.26 0.22 ...
##  $ citricacid        : num  0.35 0.43 0.49 0.24 0.44 0.11 0 0.33 0.33 0.2 ...
##  $ residualsugar     : num  7.7 1.6 2.2 4.8 18.8 ...
##  $ chlorides         : num  0.031 0.041 0.063 0.041 0.057 0.075 0.069 0.068 0.027 0.035 ...
##  $ freesulfurdioxide : num  36 29 18 30 65 16 4 34 46 58 ...
##  $ totalsulfurdioxide: num  135 114 40 113 224 49 8 102 113 184 ...
##  $ density           : num  0.994 0.99 0.998 0.994 1 ...
##  $ pH                : num  3.19 3.23 3.14 3.42 3.11 3.36 3.33 3.27 3.35 3.11 ...
##  $ sulphates         : num  0.37 0.44 0.51 0.4 0.53 0.79 0.37 0.78 0.43 0.53 ...
##  $ alcohol           : num  10.5 12.6 9.8 9.4 9.1 9.5 10.4 12.8 11.4 9 ...
##  $ quality           : int  5 6 6 6 5 5 4 6 7 6 ...
##  $ Vinho             : Factor w/ 2 levels "RED","WHITE": 2 2 1 2 2 1 1 1 2 2 ...
#mostra as vari·veis
names(Vinhos)
##  [1] "fixedacidity"       "volatileacidity"    "citricacid"        
##  [4] "residualsugar"      "chlorides"          "freesulfurdioxide" 
##  [7] "totalsulfurdioxide" "density"            "pH"                
## [10] "sulphates"          "alcohol"            "quality"           
## [13] "Vinho"
#XX Variáveis e muita informação
attach(Vinhos)

# FrequÍncia absoluta 
table(as.factor(Vinhos$quality), Vinhos$Vinho, useNA = "ifany")
##    
##      RED WHITE
##   3   10    20
##   4   53   163
##   5  681  1457
##   6  638  2198
##   7  199   880
##   8   18   175
##   9    0     5
table(as.factor(Vinhos$quality), Vinhos$Vinho)
##    
##      RED WHITE
##   3   10    20
##   4   53   163
##   5  681  1457
##   6  638  2198
##   7  199   880
##   8   18   175
##   9    0     5

Análise:

Avaliando as duas tabelas de frequência das notas/qualiade que comparam os vinhos tintos e brancos, vemos que não exsitem valores “brancos/NA” já que as duas tabelas apresentam as mesmas frequências.

Olhando os valores entre as duas tabelas, testamos a hipótese da resposta de qualidade ser diverente entre os vinhos Brancos e Tintos. Para isso fizemos um Teste para duas amostras

Quality <- split(Vinhos, Vinhos$Vinho)

t.test(Quality$WHITE$quality, Quality$RED$quality)
## 
##  Welch Two Sample t-test
## 
## data:  Quality$WHITE$quality and Quality$RED$quality
## t = 10.149, df = 2950.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1951564 0.2886173
## sample estimates:
## mean of x mean of y 
##  5.877909  5.636023

Análise:

A partir do valor do p-value e risco alfa máximo de 5%, podemos dizer que os vinhos Brancos e Tintos tem valores médios de notas diferentes, já que o p-value < 2.2e-16

# 2-Way Cross Tabulation
library(gmodels)
## Warning: package 'gmodels' was built under R version 3.4.4
CrossTable(as.factor(Vinhos$quality), Vinhos$Vinho) 
## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## | Chi-square contribution |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  6497 
## 
##  
##                           | Vinhos$Vinho 
## as.factor(Vinhos$quality) |       RED |     WHITE | Row Total | 
## --------------------------|-----------|-----------|-----------|
##                         3 |        10 |        20 |        30 | 
##                           |     0.927 |     0.303 |           | 
##                           |     0.333 |     0.667 |     0.005 | 
##                           |     0.006 |     0.004 |           | 
##                           |     0.002 |     0.003 |           | 
## --------------------------|-----------|-----------|-----------|
##                         4 |        53 |       163 |       216 | 
##                           |     0.000 |     0.000 |           | 
##                           |     0.245 |     0.755 |     0.033 | 
##                           |     0.033 |     0.033 |           | 
##                           |     0.008 |     0.025 |           | 
## --------------------------|-----------|-----------|-----------|
##                         5 |       681 |      1457 |      2138 | 
##                           |    45.546 |    14.869 |           | 
##                           |     0.319 |     0.681 |     0.329 | 
##                           |     0.426 |     0.297 |           | 
##                           |     0.105 |     0.224 |           | 
## --------------------------|-----------|-----------|-----------|
##                         6 |       638 |      2198 |      2836 | 
##                           |     5.154 |     1.683 |           | 
##                           |     0.225 |     0.775 |     0.437 | 
##                           |     0.399 |     0.449 |           | 
##                           |     0.098 |     0.338 |           | 
## --------------------------|-----------|-----------|-----------|
##                         7 |       199 |       880 |      1079 | 
##                           |    16.681 |     5.446 |           | 
##                           |     0.184 |     0.816 |     0.166 | 
##                           |     0.124 |     0.180 |           | 
##                           |     0.031 |     0.135 |           | 
## --------------------------|-----------|-----------|-----------|
##                         8 |        18 |       175 |       193 | 
##                           |    18.321 |     5.981 |           | 
##                           |     0.093 |     0.907 |     0.030 | 
##                           |     0.011 |     0.036 |           | 
##                           |     0.003 |     0.027 |           | 
## --------------------------|-----------|-----------|-----------|
##                         9 |         0 |         5 |         5 | 
##                           |     1.231 |     0.402 |           | 
##                           |     0.000 |     1.000 |     0.001 | 
##                           |     0.000 |     0.001 |           | 
##                           |     0.000 |     0.001 |           | 
## --------------------------|-----------|-----------|-----------|
##              Column Total |      1599 |      4898 |      6497 | 
##                           |     0.246 |     0.754 |           | 
## --------------------------|-----------|-----------|-----------|
## 
## 

Análise:

A partir da tabela cruzada entre tipo do vinho (Branco e Tinto) e as notas de qualidade, podemos perceber a maior frequencia geral é de notas 6 (43,7%).

Mas olhando para cada tipo de vinho individualmente, a nota 6 é mais frequente para o vinho branco(44,9%), enquanto a nota mais frenquente para o vinho tinto é 5 (42,6%), o que ajuda a confirmar a diferença entre os vinhos, com relação as notas de qualidade.

summary(Vinhos)
##   fixedacidity    volatileacidity    citricacid     residualsugar  
##  Min.   : 3.800   Min.   :0.0800   Min.   :0.0000   Min.   : 0.60  
##  1st Qu.: 6.400   1st Qu.:0.2300   1st Qu.:0.2500   1st Qu.: 1.80  
##  Median : 7.000   Median :0.2900   Median :0.3100   Median : 3.00  
##  Mean   : 7.215   Mean   :0.3397   Mean   :0.3186   Mean   : 5.44  
##  3rd Qu.: 7.700   3rd Qu.:0.4000   3rd Qu.:0.3900   3rd Qu.: 8.10  
##  Max.   :15.900   Max.   :1.5800   Max.   :1.6600   Max.   :45.80  
##    chlorides       freesulfurdioxide totalsulfurdioxide    density      
##  Min.   :0.00900   Min.   :  1.00    Min.   :  6.0      Min.   :0.9871  
##  1st Qu.:0.03800   1st Qu.: 17.00    1st Qu.: 77.0      1st Qu.:0.9923  
##  Median :0.04700   Median : 29.00    Median :118.0      Median :0.9949  
##  Mean   :0.05603   Mean   : 30.53    Mean   :115.7      Mean   :0.9947  
##  3rd Qu.:0.06500   3rd Qu.: 41.00    3rd Qu.:156.0      3rd Qu.:0.9970  
##  Max.   :0.61100   Max.   :289.00    Max.   :440.0      Max.   :1.0140  
##        pH          sulphates         alcohol           quality     
##  Min.   :2.720   Min.   :0.2200   Min.   : 0.9567   Min.   :3.000  
##  1st Qu.:3.110   1st Qu.:0.4300   1st Qu.: 9.5000   1st Qu.:5.000  
##  Median :3.210   Median :0.5100   Median :10.3000   Median :6.000  
##  Mean   :3.219   Mean   :0.5313   Mean   :10.4862   Mean   :5.818  
##  3rd Qu.:3.320   3rd Qu.:0.6000   3rd Qu.:11.3000   3rd Qu.:6.000  
##  Max.   :4.010   Max.   :2.0000   Max.   :14.9000   Max.   :9.000  
##    Vinho     
##  RED  :1599  
##  WHITE:4898  
##              
##              
##              
## 

Análise:

Olhando as estatísticas básicas de todas as proprieddes, podemos perceber alguns pontos:

aggregate (Vinhos,
           by = list(Vinho),
           FUN =  "mean")
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA

## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
##   Group.1 fixedacidity volatileacidity citricacid residualsugar  chlorides
## 1     RED     8.319637       0.5278205  0.2709756      2.538806 0.08746654
## 2   WHITE     6.854788       0.2782411  0.3341915      6.387332 0.04577236
##   freesulfurdioxide totalsulfurdioxide   density       pH sulphates
## 1          15.87492           46.46779 0.9967467 3.311113 0.6581488
## 2          35.30808          138.36066 0.9940223 3.188267 0.4898469
##    alcohol  quality Vinho
## 1 10.40008 5.636023    NA
## 2 10.51427 5.877909    NA

Análise:

Função retorna a media de todas as vaiáveis numéricas para os vinhos Brancos e Tintos Pontos que chamam a atenção:

O cometário “argument is not numeric or logical: returning NAargument is not numeric or logical: returning NA” é devido a variável vinho que não é numérica

mean(Vinhos$fixedacidity) # mÈdia
## [1] 7.215307
median(Vinhos$fixedacidity) # mÈdiana
## [1] 7
quantile(Vinhos$fixedacidity,type=4)  # Quartis
##   0%  25%  50%  75% 100% 
##  3.8  6.4  7.0  7.7 15.9
quantile(Vinhos$fixedacidity,.65,type=4) # exato percentil
## 65% 
## 7.3
range(Vinhos$fixedacidity)  # amplitude
## [1]  3.8 15.9
diff(range(Vinhos$fixedacidity)) #diferenÁa entre o maior e o menor valor
## [1] 12.1
min(Vinhos$fixedacidity)  # valor mÌnimo de x
## [1] 3.8
max(Vinhos$fixedacidity)  # valor m·ximo de x
## [1] 15.9
var(Vinhos$fixedacidity) # para obter a vari‚ncia
## [1] 1.68074
sd(Vinhos$fixedacidity)  # para obter o desvio padr„o
## [1] 1.296434
CV_fixedacidity<-sd(Vinhos$fixedacidity)/mean(Vinhos$fixedacidity)*100  # para obter o coefiiente de variaÁ„o
CV_fixedacidity
## [1] 17.96783

Análise:

As funções retornam estaísticas decritivas para a variavel fixedacidity, inclusive o Coeficiente de Variação (CV).

CV = Em teoria das probabilidades e estatística, o coeficiente de variação (CV), também conhecido como desvio padrão relativo (DPR), é uma medida padronizada de dispersão de uma distribuição de probabilidade ou de uma distribuição de frequências. É frequentemente expresso como uma porcentagem, sendo definido como a razão do desvio padrão pela média (ou seu valor absoluto. O CV ou DPR é amplamente usado em química analítica para expressar a precisão e a repetitividade de um ensaio. Também é comumente usado em campos como engenharia e física quando se fazem estudos de garantia de qualidade e avaliações de repetitividade e reprodutibilidade. O CV também é usado por economistas e investidores em modelos econômicos e na determinação da volatilidade de um valor mobiliário. Fonte: Wikipédia

#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
hist(fixedacidity)
hist(volatileacidity)
hist(citricacid )
hist(residualsugar)
hist(chlorides)
hist(freesulfurdioxide)
hist(totalsulfurdioxide)
hist(density)
hist(pH)
hist(sulphates)
hist(alcohol)
hist(quality)

Análise:

Avaliando os histogrmas, alguns pontos chamam a atenção:

hist(quality, col=c("pink"), col.main="darkgray", prob=T)

Análise:

attach(Vinhos)
## The following objects are masked from Vinhos (pos = 4):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(Vinhos$quality, main='quality')

Análise:

As análises dos Box Plots validam as que já fizemos para os histogramas.

Apesar de todos os Box Plots apresentarem Outliers, que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide. citricacid, freesulfurdioxide e alcohol com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.

Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.

boxplot(quality ~ Vinho, main='quality')

boxplot(fixedacidity ~ Vinho, main='fixedacidity',col=c('red','blue'))

boxplot(volatileacidity ~ Vinho , main='volatileacidity')

boxplot(citricacid ~ Vinho, main='citricacid')

boxplot(residualsugar ~ Vinho, main='residualsugar',col=c('red','blue'))

boxplot(chlorides ~ Vinho, main='chlorides')

boxplot(freesulfurdioxide ~ Vinho, main='freesulfurdioxide')

boxplot(totalsulfurdioxide ~ Vinho, main='totalsulfurdioxide')

boxplot(density ~ Vinho, main='density')

boxplot(pH ~ Vinho, main='pH')

boxplot(sulphates ~ Vinho, main='sulphates')

boxplot(alcohol ~ Vinho, main='alcohol')

Análise:

Os Box Plots para todas as características, agora comparando os vinhos brancos e tintos podem servir para entender características que podem distinguir entre estes dois tipos e vinhos, como já fizemos com a quality, usando o teste de hipótese.

Olhando os Box Plots, outras características que podem ser diferentes por tipo de vinho são: volatileacidity, chlorides, freesulfurdioxide e totalsulfurdioxide (já comentado nas estatísticas descritivas)

# Gr·fico de dispers„o ( pch=caracter, lwd=largura)

plot(freesulfurdioxide~totalsulfurdioxide)

plot(freesulfurdioxide~totalsulfurdioxide, pch=1, lwd=3)

plot(freesulfurdioxide~totalsulfurdioxide)
abline(h=mean(freesulfurdioxide), col="red")
abline(v=mean(totalsulfurdioxide), col="green")

Análise:

O Gráfico de dispersão mostra a relação de previsão entre as variáveis. Neste caso entre freesulfurdioxide e totalsulfurdioxide.

Estas variáveis aparentam ter uma correlação forte (núvem de pontos com pouca dispersão) e positiva (inclinação positiva/coeficiente angular > 0), indicando que a partir da informação sobre totalsulfurdioxide pode prever o valor de freesulfurdioxide, com boa acuracidade.

A linha verde representa a média do totalsulfurdioxide e a vermelha a média do freesulfurdioxide. O ponto onde onde as retas se encontram é um dos pontos que fará parte da regressão linear entre as variáveis e da uma ideia de centramento desta relação

attach(Vinhos)
## The following objects are masked from Vinhos (pos = 3):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
## The following objects are masked from Vinhos (pos = 5):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
Vinhos$fx_redSugar <- cut(residualsugar,breaks=c(0,10,20,30,max(residualsugar)))  
Vinhos$fx_redSugar  
##    [1] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##    [7] (0,10]    (0,10]    (0,10]    (20,30]   (0,10]    (0,10]   
##   [13] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [19] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##   [25] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##   [31] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [37] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (20,30]  
##   [43] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
##   [49] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [55] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [61] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##   [67] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##   [73] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [79] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##   [85] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##   [91] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##   [97] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [103] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [109] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [115] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [121] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
##  [127] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [133] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
##  [139] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (10,20]  
##  [145] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [151] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [157] (10,20]   (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
##  [163] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [169] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [175] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [181] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [187] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [193] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [199] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [205] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
##  [211] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [217] (10,20]   (0,10]    (0,10]    (20,30]   (10,20]   (10,20]  
##  [223] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [229] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
##  [235] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
##  [241] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [247] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [253] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
##  [259] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [265] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [271] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [277] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [283] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [289] (10,20]   (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
##  [295] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [301] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
##  [307] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [313] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [319] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [325] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [331] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [337] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
##  [343] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [349] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [355] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [361] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [367] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
##  [373] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [379] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [385] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [391] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [397] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [403] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [409] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [415] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [421] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [427] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [433] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
##  [439] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [445] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [451] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [457] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [463] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [469] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [475] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [481] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [487] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [493] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [499] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [505] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [511] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [517] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
##  [523] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [529] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [535] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [541] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [547] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [553] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [559] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
##  [565] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [571] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [577] (10,20]   (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
##  [583] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [589] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
##  [595] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (10,20]  
##  [601] (0,10]    (0,10]    (20,30]   (10,20]   (0,10]    (0,10]   
##  [607] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [613] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [619] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [625] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [631] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
##  [637] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
##  [643] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [649] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [655] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [661] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [667] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [673] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [679] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [685] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [691] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [697] (10,20]   (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
##  [703] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [709] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [715] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [721] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
##  [727] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [733] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [739] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [745] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [751] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [757] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [763] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [769] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [775] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [781] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [787] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [793] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [799] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [805] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [811] (0,10]    (10,20]   (10,20]   (0,10]    (10,20]   (10,20]  
##  [817] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [823] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [829] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [835] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
##  [841] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
##  [847] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [853] (0,10]    (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
##  [859] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [865] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [871] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
##  [877] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [883] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [889] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [895] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [901] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
##  [907] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [913] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [919] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [925] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [931] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
##  [937] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
##  [943] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [949] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [955] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [961] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
##  [967] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
##  [973] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [979] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
##  [985] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [991] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
##  [997] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1003] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1009] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1015] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1021] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1027] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1033] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [1039] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1045] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1051] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1057] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1063] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1069] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1075] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1081] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1087] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1093] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1099] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1105] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [1111] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1117] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1123] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1129] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [1135] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1141] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1147] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [1153] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1159] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1165] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1171] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1177] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1183] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1189] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1195] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1201] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1207] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [1213] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1219] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [1225] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [1231] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1237] (0,10]    (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [1243] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [1249] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1255] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1261] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1267] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1273] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1279] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1285] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1291] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (10,20]  
## [1297] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1303] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [1309] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1315] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (10,20]  
## [1321] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1327] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1333] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1339] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1345] (10,20]   (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [1351] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1357] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1363] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1369] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1375] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1381] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1387] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1393] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [1399] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1405] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1411] (10,20]   (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [1417] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (20,30]  
## [1423] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1429] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1435] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1441] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [1447] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [1453] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1459] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1465] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1471] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1477] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [1483] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1489] (0,10]    (10,20]   (20,30]   (0,10]    (0,10]    (0,10]   
## [1495] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1501] (0,10]    (0,10]    (10,20]   (0,10]    (30,45.8] (0,10]   
## [1507] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1513] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1519] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1525] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1531] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1537] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1543] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1549] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [1555] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1561] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1567] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1573] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1579] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1585] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1591] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1597] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1603] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1609] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1615] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1621] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1627] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1633] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1639] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1645] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1651] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1657] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1663] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1669] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1675] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [1681] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1687] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1693] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1699] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1705] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1711] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1717] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1723] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1729] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [1735] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1741] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1747] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1753] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1759] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1765] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [1771] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1777] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1783] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [1789] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1795] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1801] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1807] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [1813] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [1819] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1825] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [1831] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1837] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1843] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [1849] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1855] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [1861] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1867] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1873] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1879] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1885] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1891] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [1897] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1903] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1909] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [1915] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1921] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1927] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1933] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1939] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1945] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [1951] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [1957] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [1963] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [1969] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [1975] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [1981] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (20,30]  
## [1987] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [1993] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [1999] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2005] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [2011] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2017] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2023] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2029] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2035] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2041] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2047] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2053] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2059] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2065] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2071] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2077] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2083] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2089] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2095] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2101] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2107] (10,20]   (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [2113] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [2119] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2125] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2131] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2137] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2143] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2149] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2155] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [2161] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [2167] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2173] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (10,20]  
## [2179] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2185] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2191] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [2197] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2203] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2209] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [2215] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2221] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2227] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2233] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2239] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2245] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2251] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2257] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2263] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (10,20]  
## [2269] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2275] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2281] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2287] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2293] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2299] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2305] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2311] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2317] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2323] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [2329] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2335] (0,10]    (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [2341] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2347] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2353] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [2359] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2365] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2371] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2377] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2383] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [2389] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2395] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [2401] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2407] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [2413] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2419] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2425] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2431] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2437] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [2443] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2449] (10,20]   (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
## [2455] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2461] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2467] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [2473] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [2479] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2485] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2491] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2497] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2503] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2509] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2515] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2521] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2527] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [2533] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2539] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2545] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2551] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2557] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2563] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2569] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2575] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2581] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2587] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2593] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2599] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2605] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2611] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2617] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2623] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [2629] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [2635] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2641] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2647] (0,10]    (20,30]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2653] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2659] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2665] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2671] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2677] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [2683] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2689] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2695] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2701] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2707] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2713] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2719] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2725] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [2731] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [2737] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2743] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2749] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2755] (10,20]   (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [2761] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [2767] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2773] (0,10]    (10,20]   (10,20]   (0,10]    (10,20]   (0,10]   
## [2779] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2785] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2791] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2797] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2803] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2809] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2815] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [2821] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [2827] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2833] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2839] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2845] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [2851] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2857] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2863] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2869] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [2875] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2881] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2887] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2893] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [2899] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [2905] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [2911] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [2917] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2923] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [2929] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [2935] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [2941] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2947] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [2953] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2959] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [2965] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2971] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [2977] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2983] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [2989] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [2995] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3001] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3007] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3013] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [3019] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3025] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3031] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3037] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3043] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3049] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3055] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3061] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [3067] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3073] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3079] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3085] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3091] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3097] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3103] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3109] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3115] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3121] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3127] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3133] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [3139] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3145] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3151] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (20,30]  
## [3157] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3163] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3169] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3175] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3181] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3187] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3193] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3199] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3205] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3211] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3217] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [3223] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3229] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3235] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3241] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3247] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3253] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3259] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3265] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3271] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3277] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3283] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3289] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3295] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3301] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3307] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3313] (10,20]   (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [3319] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3325] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3331] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [3337] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3343] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3349] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [3355] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3361] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3367] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3373] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3379] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3385] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3391] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3397] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3403] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3409] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [3415] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3421] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [3427] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [3433] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3439] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3445] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [3451] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3457] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [3463] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3469] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [3475] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3481] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3487] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3493] (0,10]    (10,20]   (10,20]   (0,10]    (10,20]   (0,10]   
## [3499] (10,20]   (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [3505] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [3511] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3517] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3523] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3529] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3535] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [3541] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3547] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3553] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [3559] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3565] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3571] (0,10]    (30,45.8] (0,10]    (0,10]    (0,10]    (0,10]   
## [3577] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3583] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3589] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3595] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3601] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3607] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3613] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [3619] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [3625] (0,10]    (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
## [3631] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3637] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [3643] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3649] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3655] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [3661] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [3667] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [3673] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3679] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3685] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3691] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3697] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3703] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3709] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3715] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3721] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3727] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3733] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3739] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3745] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3751] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [3757] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3763] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (10,20]  
## [3769] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3775] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (10,20]  
## [3781] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3787] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3793] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [3799] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [3805] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3811] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3817] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3823] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [3829] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [3835] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (30,45.8]
## [3841] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [3847] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3853] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3859] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3865] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [3871] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3877] (10,20]   (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [3883] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [3889] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [3895] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3901] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [3907] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3913] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3919] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3925] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3931] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [3937] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3943] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3949] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3955] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3961] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3967] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3973] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [3979] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3985] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [3991] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [3997] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4003] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4009] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (10,20]  
## [4015] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [4021] (0,10]    (10,20]   (20,30]   (0,10]    (10,20]   (10,20]  
## [4027] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4033] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4039] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4045] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4051] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4057] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4063] (10,20]   (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [4069] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4075] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4081] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4087] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4093] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4099] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4105] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [4111] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4117] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4123] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4129] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4135] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [4141] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4147] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4153] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4159] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [4165] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (10,20]  
## [4171] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4177] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4183] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4189] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [4195] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4201] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4207] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4213] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4219] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4225] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4231] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [4237] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4243] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4249] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4255] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4261] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4267] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4273] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4279] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4285] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [4291] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4297] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4303] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4309] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4315] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4321] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4327] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4333] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [4339] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4345] (0,10]    (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
## [4351] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4357] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4363] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4369] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4375] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4381] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4387] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4393] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4399] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4405] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4411] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [4417] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4423] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4429] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [4435] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4441] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [4447] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [4453] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [4459] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4465] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4471] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [4477] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4483] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4489] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4495] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4501] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4507] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4513] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4519] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4525] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [4531] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4537] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4543] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4549] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4555] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4561] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4567] (0,10]    (10,20]   (10,20]   (0,10]    (10,20]   (0,10]   
## [4573] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4579] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4585] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [4591] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4597] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4603] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4609] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4615] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4621] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4627] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4633] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4639] (10,20]   (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [4645] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4651] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [4657] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4663] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4669] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [4675] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4681] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4687] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4693] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4699] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4705] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4711] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4717] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (10,20]  
## [4723] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (10,20]  
## [4729] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4735] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [4741] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4747] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [4753] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4759] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4765] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4771] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [4777] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4783] (10,20]   (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [4789] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [4795] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4801] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4807] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [4813] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [4819] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4825] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [4831] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [4837] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4843] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4849] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [4855] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [4861] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4867] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (0,10]   
## [4873] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4879] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4885] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [4891] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4897] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [4903] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4909] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4915] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (20,30]  
## [4921] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4927] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [4933] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [4939] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [4945] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [4951] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [4957] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [4963] (0,10]    (20,30]   (10,20]   (10,20]   (10,20]   (0,10]   
## [4969] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [4975] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4981] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [4987] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4993] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [4999] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5005] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5011] (10,20]   (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [5017] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5023] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5029] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5035] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5041] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [5047] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5053] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5059] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5065] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5071] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5077] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5083] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5089] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5095] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [5101] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5107] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5113] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [5119] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5125] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5131] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5137] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5143] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5149] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5155] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5161] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5167] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5173] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5179] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5185] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5191] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5197] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5203] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5209] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5215] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5221] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5227] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5233] (0,10]    (0,10]    (20,30]   (0,10]    (0,10]    (0,10]   
## [5239] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5245] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5251] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [5257] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5263] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [5269] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5275] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [5281] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5287] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [5293] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5299] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5305] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5311] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [5317] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [5323] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5329] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [5335] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5341] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5347] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5353] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5359] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [5365] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5371] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5377] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5383] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5389] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5395] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5401] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5407] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5413] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [5419] (0,10]    (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [5425] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5431] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5437] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5443] (0,10]    (20,30]   (0,10]    (0,10]    (0,10]    (10,20]  
## [5449] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5455] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [5461] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5467] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5473] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5479] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5485] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5491] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5497] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5503] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [5509] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5515] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5521] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5527] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5533] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5539] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5545] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5551] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5557] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5563] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5569] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5575] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (10,20]  
## [5581] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5587] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5593] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5599] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5605] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5611] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5617] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5623] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5629] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5635] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5641] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [5647] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5653] (20,30]   (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [5659] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5665] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5671] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (10,20]  
## [5677] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5683] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5689] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5695] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5701] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [5707] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5713] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5719] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (10,20]  
## [5725] (0,10]    (10,20]   (0,10]    (10,20]   (0,10]    (10,20]  
## [5731] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5737] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5743] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5749] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [5755] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5761] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [5767] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5773] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5779] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5785] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [5791] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [5797] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5803] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [5809] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5815] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5821] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5827] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5833] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5839] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [5845] (0,10]    (0,10]    (10,20]   (10,20]   (10,20]   (0,10]   
## [5851] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [5857] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5863] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [5869] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5875] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5881] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (10,20]  
## [5887] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [5893] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5899] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5905] (10,20]   (0,10]    (0,10]    (10,20]   (10,20]   (10,20]  
## [5911] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [5917] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [5923] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5929] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5935] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5941] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5947] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [5953] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (10,20]  
## [5959] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5965] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [5971] (10,20]   (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [5977] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5983] (0,10]    (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [5989] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [5995] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6001] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6007] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6013] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [6019] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6025] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6031] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [6037] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6043] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6049] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [6055] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [6061] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [6067] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6073] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6079] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6085] (10,20]   (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6091] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6097] (10,20]   (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6103] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [6109] (0,10]    (10,20]   (10,20]   (0,10]    (0,10]    (0,10]   
## [6115] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [6121] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6127] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6133] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6139] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [6145] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [6151] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6157] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6163] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [6169] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [6175] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6181] (10,20]   (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [6187] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6193] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [6199] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6205] (0,10]    (10,20]   (10,20]   (10,20]   (0,10]    (0,10]   
## [6211] (0,10]    (0,10]    (10,20]   (10,20]   (0,10]    (0,10]   
## [6217] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6223] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6229] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6235] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6241] (0,10]    (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [6247] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [6253] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6259] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [6265] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6271] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (10,20]  
## [6277] (10,20]   (0,10]    (10,20]   (0,10]    (10,20]   (0,10]   
## [6283] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6289] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [6295] (10,20]   (0,10]    (0,10]    (10,20]   (10,20]   (10,20]  
## [6301] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6307] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6313] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [6319] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [6325] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6331] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6337] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6343] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6349] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6355] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6361] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [6367] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6373] (10,20]   (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [6379] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6385] (0,10]    (0,10]    (0,10]    (10,20]   (10,20]   (0,10]   
## [6391] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6397] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6403] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [6409] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6415] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (10,20]  
## [6421] (10,20]   (10,20]   (0,10]    (0,10]    (10,20]   (0,10]   
## [6427] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6433] (0,10]    (0,10]    (0,10]    (0,10]    (10,20]   (0,10]   
## [6439] (10,20]   (0,10]    (10,20]   (0,10]    (0,10]    (0,10]   
## [6445] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [6451] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (0,10]   
## [6457] (0,10]    (0,10]    (0,10]    (10,20]   (0,10]    (10,20]  
## [6463] (0,10]    (10,20]   (0,10]    (0,10]    (0,10]    (0,10]   
## [6469] (0,10]    (0,10]    (10,20]   (0,10]    (0,10]    (10,20]  
## [6475] (0,10]    (10,20]   (0,10]    (10,20]   (10,20]   (0,10]   
## [6481] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6487] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## [6493] (0,10]    (0,10]    (0,10]    (0,10]    (0,10]   
## Levels: (0,10] (10,20] (20,30] (30,45.8]
str(Vinhos)
## 'data.frame':    6497 obs. of  14 variables:
##  $ fixedacidity      : num  6.6 6.7 10.6 5.4 6.7 6.8 6.6 7.2 5.1 6.2 ...
##  $ volatileacidity   : num  0.24 0.34 0.31 0.18 0.3 0.5 0.61 0.66 0.26 0.22 ...
##  $ citricacid        : num  0.35 0.43 0.49 0.24 0.44 0.11 0 0.33 0.33 0.2 ...
##  $ residualsugar     : num  7.7 1.6 2.2 4.8 18.8 ...
##  $ chlorides         : num  0.031 0.041 0.063 0.041 0.057 0.075 0.069 0.068 0.027 0.035 ...
##  $ freesulfurdioxide : num  36 29 18 30 65 16 4 34 46 58 ...
##  $ totalsulfurdioxide: num  135 114 40 113 224 49 8 102 113 184 ...
##  $ density           : num  0.994 0.99 0.998 0.994 1 ...
##  $ pH                : num  3.19 3.23 3.14 3.42 3.11 3.36 3.33 3.27 3.35 3.11 ...
##  $ sulphates         : num  0.37 0.44 0.51 0.4 0.53 0.79 0.37 0.78 0.43 0.53 ...
##  $ alcohol           : num  10.5 12.6 9.8 9.4 9.1 9.5 10.4 12.8 11.4 9 ...
##  $ quality           : int  5 6 6 6 5 5 4 6 7 6 ...
##  $ Vinho             : Factor w/ 2 levels "RED","WHITE": 2 2 1 2 2 1 1 1 2 2 ...
##  $ fx_redSugar       : Factor w/ 4 levels "(0,10]","(10,20]",..: 1 1 1 1 2 1 1 1 1 3 ...
CrossTable( Vinhos$fx_redSugar , Vinhos$Vinho) 
## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## | Chi-square contribution |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  6497 
## 
##  
##                    | Vinhos$Vinho 
## Vinhos$fx_redSugar |       RED |     WHITE | Row Total | 
## -------------------|-----------|-----------|-----------|
##             (0,10] |      1588 |      3705 |      5293 | 
##                    |    62.493 |    20.401 |           | 
##                    |     0.300 |     0.700 |     0.815 | 
##                    |     0.993 |     0.756 |           | 
##                    |     0.244 |     0.570 |           | 
## -------------------|-----------|-----------|-----------|
##            (10,20] |        11 |      1175 |      1186 | 
##                    |   270.305 |    88.244 |           | 
##                    |     0.009 |     0.991 |     0.183 | 
##                    |     0.007 |     0.240 |           | 
##                    |     0.002 |     0.181 |           | 
## -------------------|-----------|-----------|-----------|
##            (20,30] |         0 |        15 |        15 | 
##                    |     3.692 |     1.205 |           | 
##                    |     0.000 |     1.000 |     0.002 | 
##                    |     0.000 |     0.003 |           | 
##                    |     0.000 |     0.002 |           | 
## -------------------|-----------|-----------|-----------|
##          (30,45.8] |         0 |         3 |         3 | 
##                    |     0.738 |     0.241 |           | 
##                    |     0.000 |     1.000 |     0.000 | 
##                    |     0.000 |     0.001 |           | 
##                    |     0.000 |     0.000 |           | 
## -------------------|-----------|-----------|-----------|
##       Column Total |      1599 |      4898 |      6497 | 
##                    |     0.246 |     0.754 |           | 
## -------------------|-----------|-----------|-----------|
## 
## 

Análise:

Olahndo os intervalos de resíduos de açucar (faixas de 10 em 10), podemos ver que a maior concentração esta na faixa entre 0 e 10 (81,5%)

O mesmo comprtamento se aplica se olharmos por tipo de vinho: Brancos (75,6%) e tintos (99,3%). O que indica que os vinhos tintos tem menos açucar, pois sua concentração esta na faixa de 0 a 10 (faixa inicial) de concentração de resíduo de açucar. E os brancos apresentam maiores concetrações nas faixas superiores: Faixa de 10 a 20, Brancos (24%) x Tintos (0,7%)

attach(Vinhos)
## The following objects are masked from Vinhos (pos = 3):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
## The following objects are masked from Vinhos (pos = 4):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
## The following objects are masked from Vinhos (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, Vinho, volatileacidity
library(psych)
## Warning: package 'psych' was built under R version 3.4.4
describe(Vinhos)
##                    vars    n   mean    sd median trimmed   mad  min    max
## fixedacidity          1 6497   7.22  1.30   7.00    7.06  0.89 3.80  15.90
## volatileacidity       2 6497   0.34  0.16   0.29    0.32  0.12 0.08   1.58
## citricacid            3 6497   0.32  0.15   0.31    0.32  0.10 0.00   1.66
## residualsugar         4 6497   5.44  4.73   3.00    4.70  2.52 0.60  45.80
## chlorides             5 6497   0.06  0.04   0.05    0.05  0.02 0.01   0.61
## freesulfurdioxide     6 6497  30.53 17.75  29.00   29.32 17.79 1.00 289.00
## totalsulfurdioxide    7 6497 115.74 56.52 118.00  115.92 57.82 6.00 440.00
## density               8 6497   0.99  0.00   0.99    0.99  0.00 0.99   1.01
## pH                    9 6497   3.22  0.16   3.21    3.21  0.16 2.72   4.01
## sulphates            10 6497   0.53  0.15   0.51    0.52  0.12 0.22   2.00
## alcohol              11 6497  10.49  1.22  10.30   10.40  1.33 0.96  14.90
## quality              12 6497   5.82  0.87   6.00    5.79  1.48 3.00   9.00
## Vinho*               13 6497   1.75  0.43   2.00    1.82  0.00 1.00   2.00
## fx_redSugar*         14 6497   1.19  0.40   1.00    1.11  0.00 1.00   4.00
##                     range  skew kurtosis   se
## fixedacidity        12.10  1.72     5.05 0.02
## volatileacidity      1.50  1.49     2.82 0.00
## citricacid           1.66  0.47     2.39 0.00
## residualsugar       45.20  1.24     1.28 0.06
## chlorides            0.60  5.40    50.84 0.00
## freesulfurdioxide  288.00  1.22     7.90 0.22
## totalsulfurdioxide 434.00  0.00    -0.37 0.70
## density              0.03  0.05    -0.32 0.00
## pH                   1.29  0.39     0.37 0.00
## sulphates            1.78  1.80     8.64 0.00
## alcohol             13.94  0.26     1.56 0.02
## quality              6.00  0.19     0.23 0.01
## Vinho*               1.00 -1.18    -0.61 0.01
## fx_redSugar*         3.00  1.81     2.20 0.00
# describe
# A data.frame of the relevant statistics:
# item name
# item number
# number of valid cases
# mean
# standard deviation
# trimmed mean (with trim defaulting to .1)
# median (standard or interpolated
# mad: median absolute deviation (from the median)
# minimum
# maximum
# skew
# kurtosis
# standard error


summary(Vinhos)
##   fixedacidity    volatileacidity    citricacid     residualsugar  
##  Min.   : 3.800   Min.   :0.0800   Min.   :0.0000   Min.   : 0.60  
##  1st Qu.: 6.400   1st Qu.:0.2300   1st Qu.:0.2500   1st Qu.: 1.80  
##  Median : 7.000   Median :0.2900   Median :0.3100   Median : 3.00  
##  Mean   : 7.215   Mean   :0.3397   Mean   :0.3186   Mean   : 5.44  
##  3rd Qu.: 7.700   3rd Qu.:0.4000   3rd Qu.:0.3900   3rd Qu.: 8.10  
##  Max.   :15.900   Max.   :1.5800   Max.   :1.6600   Max.   :45.80  
##    chlorides       freesulfurdioxide totalsulfurdioxide    density      
##  Min.   :0.00900   Min.   :  1.00    Min.   :  6.0      Min.   :0.9871  
##  1st Qu.:0.03800   1st Qu.: 17.00    1st Qu.: 77.0      1st Qu.:0.9923  
##  Median :0.04700   Median : 29.00    Median :118.0      Median :0.9949  
##  Mean   :0.05603   Mean   : 30.53    Mean   :115.7      Mean   :0.9947  
##  3rd Qu.:0.06500   3rd Qu.: 41.00    3rd Qu.:156.0      3rd Qu.:0.9970  
##  Max.   :0.61100   Max.   :289.00    Max.   :440.0      Max.   :1.0140  
##        pH          sulphates         alcohol           quality     
##  Min.   :2.720   Min.   :0.2200   Min.   : 0.9567   Min.   :3.000  
##  1st Qu.:3.110   1st Qu.:0.4300   1st Qu.: 9.5000   1st Qu.:5.000  
##  Median :3.210   Median :0.5100   Median :10.3000   Median :6.000  
##  Mean   :3.219   Mean   :0.5313   Mean   :10.4862   Mean   :5.818  
##  3rd Qu.:3.320   3rd Qu.:0.6000   3rd Qu.:11.3000   3rd Qu.:6.000  
##  Max.   :4.010   Max.   :2.0000   Max.   :14.9000   Max.   :9.000  
##    Vinho         fx_redSugar  
##  RED  :1599   (0,10]   :5293  
##  WHITE:4898   (10,20]  :1186  
##               (20,30]  :  15  
##               (30,45.8]:   3  
##                               
## 
white <- subset(Vinhos, Vinho=="WHITE", select=c(quality,fixedacidity,volatileacidity,citricacid,residualsugar,
                                                 chlorides,freesulfurdioxide,totalsulfurdioxide,density,pH,
                                                 sulphates,alcohol))

Análise:

Criamos um Dataset para os vinhos Brancos, com todas as variáveis usadas anteriormente

#EstatÌsticas descritivas
summary(white)
##     quality       fixedacidity    volatileacidity    citricacid    
##  Min.   :3.000   Min.   : 3.800   Min.   :0.0800   Min.   :0.0000  
##  1st Qu.:5.000   1st Qu.: 6.300   1st Qu.:0.2100   1st Qu.:0.2700  
##  Median :6.000   Median : 6.800   Median :0.2600   Median :0.3200  
##  Mean   :5.878   Mean   : 6.855   Mean   :0.2782   Mean   :0.3342  
##  3rd Qu.:6.000   3rd Qu.: 7.300   3rd Qu.:0.3200   3rd Qu.:0.3900  
##  Max.   :9.000   Max.   :14.200   Max.   :1.1000   Max.   :1.6600  
##  residualsugar      chlorides       freesulfurdioxide totalsulfurdioxide
##  Min.   : 0.600   Min.   :0.00900   Min.   :  2.00    Min.   :  9.0     
##  1st Qu.: 1.700   1st Qu.:0.03600   1st Qu.: 23.00    1st Qu.:108.0     
##  Median : 5.200   Median :0.04300   Median : 34.00    Median :134.0     
##  Mean   : 6.387   Mean   :0.04577   Mean   : 35.31    Mean   :138.4     
##  3rd Qu.: 9.900   3rd Qu.:0.05000   3rd Qu.: 46.00    3rd Qu.:167.0     
##  Max.   :45.800   Max.   :0.34600   Max.   :289.00    Max.   :440.0     
##     density             pH          sulphates         alcohol     
##  Min.   :0.9871   Min.   :2.720   Min.   :0.2200   Min.   : 8.00  
##  1st Qu.:0.9917   1st Qu.:3.090   1st Qu.:0.4100   1st Qu.: 9.50  
##  Median :0.9937   Median :3.180   Median :0.4700   Median :10.40  
##  Mean   :0.9940   Mean   :3.188   Mean   :0.4898   Mean   :10.51  
##  3rd Qu.:0.9961   3rd Qu.:3.280   3rd Qu.:0.5500   3rd Qu.:11.40  
##  Max.   :1.0140   Max.   :3.820   Max.   :1.0800   Max.   :14.20
str(white)
## 'data.frame':    4898 obs. of  12 variables:
##  $ quality           : int  5 6 6 5 7 6 5 6 6 6 ...
##  $ fixedacidity      : num  6.6 6.7 5.4 6.7 5.1 6.2 6.6 7.3 6.7 6.2 ...
##  $ volatileacidity   : num  0.24 0.34 0.18 0.3 0.26 0.22 0.25 0.27 0.26 0.12 ...
##  $ citricacid        : num  0.35 0.43 0.24 0.44 0.33 0.2 0.36 0.37 0.29 0.26 ...
##  $ residualsugar     : num  7.7 1.6 4.8 18.8 1.1 ...
##  $ chlorides         : num  0.031 0.041 0.041 0.057 0.027 0.035 0.045 0.042 0.038 0.044 ...
##  $ freesulfurdioxide : num  36 29 30 65 46 58 54 36 40 56 ...
##  $ totalsulfurdioxide: num  135 114 113 224 113 184 180 130 179 158 ...
##  $ density           : num  0.994 0.99 0.994 1 0.989 ...
##  $ pH                : num  3.19 3.23 3.42 3.11 3.35 3.11 3.08 3.48 3.23 3.52 ...
##  $ sulphates         : num  0.37 0.44 0.4 0.53 0.43 0.53 0.42 0.75 0.56 0.37 ...
##  $ alcohol           : num  10.5 12.6 9.4 9.1 11.4 9 9.2 9.9 10.4 10.5 ...

Análise:

Olhando as estatísticas básicas de todas as proprieddes dos vinhos brancos, podemos perceber alguns pontos:

attach(white)
## The following objects are masked from Vinhos (pos = 4):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 5):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 8):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
#EstatÌsticas descritivas

par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(quality, main='quality')

Análise:

Todos os Box Plots dos vinhos brancos apresentarem Outliers (exceto a variavel alcohol), que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide, citricacid e freesulfurdioxide com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.

Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.

boxplot.stats(white$residualsugar)
## $stats
## [1]  0.6  1.7  5.2  9.9 22.0
## 
## $n
## [1] 4898
## 
## $conf
## [1] 5.014877 5.385123
## 
## $out
## [1] 26.05 31.60 22.60 45.80 31.60 26.05 23.50
AIQ_residualsugar<-quantile(white$residualsugar,.75,type=2)-quantile(white$residualsugar,.25,type=2)
AIQ_residualsugar
## 75% 
## 8.2
limsup_residualsugar= quantile(white$residualsugar,.75,type=4)+1.5*AIQ_residualsugar
limsup_residualsugar
##  75% 
## 22.2
liminf_residualsugar= quantile(white$residualsugar,.25,type=2)-1.5*AIQ_residualsugar
liminf_residualsugar
##   25% 
## -10.6

Análise:

Sobre as estatísticas do BoxPlot (boxplot.stat) podemos dizer: - O bigode inferiro = valor mínimo (0,6), os qurtis Q1 = 1,7 e Q2 (mediana) = 5,2 e Q3 = 9,9. O bigode superior = 22,0. Como temos valores maiores que o 22,0, teremos outliers acima de 22,0. Mostrado no $out. - Os valores do $conf, são (segundo Chambers e McGill) aproximadamente o intervalo de confiança para a mediana.

Temos também a amplitude entre quartis: Q3 - Q1 = 8,2

#excluir outliers

plot(quality~residualsugar)

white1<-subset(white, residualsugar<=22.2)   

#fix(white1)

Análise:

Analisando o gráfico do residuo de açucar (resildualsugar) x nota de qualidade dos vinhos brancos (quality), podemos perceber uma maior concentração de resíduos de açucar para os vinhos com notas entre 5 e 6

attach(white1)
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 5):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 7):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 9):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
summary(white1)
##     quality       fixedacidity    volatileacidity   citricacid    
##  Min.   :3.000   Min.   : 3.800   Min.   :0.080   Min.   :0.0000  
##  1st Qu.:5.000   1st Qu.: 6.300   1st Qu.:0.210   1st Qu.:0.2700  
##  Median :6.000   Median : 6.800   Median :0.260   Median :0.3200  
##  Mean   :5.878   Mean   : 6.854   Mean   :0.278   Mean   :0.3341  
##  3rd Qu.:6.000   3rd Qu.: 7.300   3rd Qu.:0.320   3rd Qu.:0.3900  
##  Max.   :9.000   Max.   :14.200   Max.   :1.100   Max.   :1.6600  
##  residualsugar      chlorides       freesulfurdioxide totalsulfurdioxide
##  Min.   : 0.600   Min.   :0.00900   Min.   :  2.00    Min.   :  9.0     
##  1st Qu.: 1.700   1st Qu.:0.03600   1st Qu.: 23.00    1st Qu.:108.0     
##  Median : 5.200   Median :0.04300   Median : 34.00    Median :134.0     
##  Mean   : 6.354   Mean   :0.04575   Mean   : 35.31    Mean   :138.3     
##  3rd Qu.: 9.850   3rd Qu.:0.05000   3rd Qu.: 46.00    3rd Qu.:167.0     
##  Max.   :22.000   Max.   :0.34600   Max.   :289.00    Max.   :440.0     
##     density             pH          sulphates         alcohol     
##  Min.   :0.9871   Min.   :2.720   Min.   :0.2200   Min.   : 8.00  
##  1st Qu.:0.9917   1st Qu.:3.090   1st Qu.:0.4100   1st Qu.: 9.50  
##  Median :0.9937   Median :3.180   Median :0.4700   Median :10.40  
##  Mean   :0.9940   Mean   :3.188   Mean   :0.4899   Mean   :10.51  
##  3rd Qu.:0.9961   3rd Qu.:3.280   3rd Qu.:0.5500   3rd Qu.:11.40  
##  Max.   :1.0024   Max.   :3.820   Max.   :1.0800   Max.   :14.20
plot(residualsugar,alcohol)
abline(v=mean(residualsugar), col="red")
abline(h=mean(alcohol), col="green")

Análise:

Após tirarmos o valor de residualsugar acima de 22,2 (7 valores acima do limite do bigode do BoxPlot), podemos analisar que existe uma correlação negativa entre as variáveis, ou seja quanto maior o teor alcolico, menor a concentração de resíduo de açucar, com exceção de valores de baixo resíduo de açucar e baixa quantidade de alcool, que possivelmente pode ser explicado por não ter açucar suficiente no início do processo (suco de uva) e que não provoca uma fermentação que eleve o nível de alcool no vinho.

Ainda observando que estes valores de residuo de açucar baixo e alcool baixo, reduzem os valores de média para as duas variáveis, podendo enviezar a interpretação de uma futura análise de regressão.

A base de dados white1 é a base de vinhos brancos sem os Outliers, que será usada a partir de agora

# matriz de correlaÁıes
matcor <- cor(white1)
print(matcor, digits = 2)
##                    quality fixedacidity volatileacidity citricacid
## quality             1.0000       -0.114         -0.1963    -0.0088
## fixedacidity       -0.1141        1.000         -0.0248     0.2895
## volatileacidity    -0.1963       -0.025          1.0000    -0.1529
## citricacid         -0.0088        0.290         -0.1529     1.0000
## residualsugar      -0.0995        0.087          0.0460     0.0914
## chlorides          -0.2095        0.023          0.0700     0.1132
## freesulfurdioxide   0.0088       -0.049         -0.0949     0.0943
## totalsulfurdioxide -0.1746        0.091          0.0892     0.1207
## density            -0.3176        0.268          0.0032     0.1483
## pH                  0.0991       -0.427         -0.0334    -0.1643
## sulphates           0.0535       -0.017         -0.0379     0.0616
## alcohol             0.4363       -0.120          0.0673    -0.0765
##                    residualsugar chlorides freesulfurdioxide
## quality                   -0.100    -0.210           0.00876
## fixedacidity               0.087     0.023          -0.04884
## volatileacidity            0.046     0.070          -0.09485
## citricacid                 0.091     0.113           0.09425
## residualsugar              1.000     0.086           0.30987
## chlorides                  0.086     1.000           0.10095
## freesulfurdioxide          0.310     0.101           1.00000
## totalsulfurdioxide         0.408     0.199           0.61591
## density                    0.831     0.261           0.30898
## pH                        -0.199    -0.091           0.00018
## sulphates                 -0.028     0.017           0.06009
## alcohol                   -0.462    -0.362          -0.25022
##                    totalsulfurdioxide density       pH sulphates alcohol
## quality                       -0.1746 -0.3176  0.09913     0.053   0.436
## fixedacidity                   0.0905  0.2682 -0.42667    -0.017  -0.120
## volatileacidity                0.0892  0.0032 -0.03342    -0.038   0.067
## citricacid                     0.1207  0.1483 -0.16430     0.062  -0.077
## residualsugar                  0.4081  0.8315 -0.19916    -0.028  -0.462
## chlorides                      0.1990  0.2613 -0.09063     0.017  -0.362
## freesulfurdioxide              0.6159  0.3090  0.00018     0.060  -0.250
## totalsulfurdioxide             1.0000  0.5436  0.00274     0.135  -0.448
## density                        0.5436  1.0000 -0.09845     0.075  -0.806
## pH                             0.0027 -0.0984  1.00000     0.155   0.121
## sulphates                      0.1348  0.0748  0.15517     1.000  -0.018
## alcohol                       -0.4484 -0.8064  0.12103    -0.018   1.000

Análise:

Observando as correlações, algumas nos chamam a atenção: - residualsugar x density = 0,8315, que comprova que vinhos com muito açucar tem maior densidade, no sentido inverso; - vinhos com muito alcool tem menor densidade (correlação = -0,8064). - forte correlação entre freesulfurdioxide x totalsulfurdioxide (0,61591), devido ao livre fazer parte do total deste conservante.

#install.packages(corrgram)
#library(corrgram)
#corrgram (matcor, type = "cor", lower.panel = panel.shade, upper.panel = panel.pie)

panel.cor <- function(x, y, digits=2, prefix ="", cex.cor,
                      ...)  {
  usr <- par("usr")
  on.exit(par(usr))
  par(usr = c(0, 1, 0, 1))
  r <- cor(x, y , use = "pairwise.complete.obs")
  txt <- format(c(r, 0.123456789), digits = digits) [1]
  txt <- paste(prefix, txt, sep = "")
  if (missing(cex.cor))
    cex <- 0.8/strwidth(txt)
  # abs(r) È para que na saÌda as correlaÁıes ficam proporcionais
  text(0.5, 0.5, txt, cex = cex * abs(r))
}
#pdf(file = "grafico.pdf")
pairs(white1, lower.panel=panel.smooth, upper.panel=panel.cor)

Análise:

Agora podemos comprovar atraves de gráficos o que já foi comentado a análise da tabela de correlação

#avaliar inicio
dados_normalizados = as.data.frame(scale(white1))

names(dados_normalizados)
##  [1] "quality"            "fixedacidity"       "volatileacidity"   
##  [4] "citricacid"         "residualsugar"      "chlorides"         
##  [7] "freesulfurdioxide"  "totalsulfurdioxide" "density"           
## [10] "pH"                 "sulphates"          "alcohol"
summary(dados_normalizados)
##     quality         fixedacidity      volatileacidity     citricacid     
##  Min.   :-3.2482   Min.   :-3.61898   Min.   :-1.9740   Min.   :-2.7613  
##  1st Qu.:-0.9910   1st Qu.:-0.65685   1st Qu.:-0.6781   1st Qu.:-0.5299  
##  Median : 0.1375   Median :-0.06443   Median :-0.1797   Median :-0.1167  
##  Mean   : 0.0000   Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.0000  
##  3rd Qu.: 0.1375   3rd Qu.: 0.52800   3rd Qu.: 0.4184   3rd Qu.: 0.4617  
##  Max.   : 3.5232   Max.   : 8.70347   Max.   : 8.1937   Max.   :10.9572  
##  residualsugar       chlorides       freesulfurdioxide  totalsulfurdioxide
##  Min.   :-1.1623   Min.   :-1.6835   Min.   :-1.95836   Min.   :-3.0434   
##  1st Qu.:-0.9401   1st Qu.:-0.4467   1st Qu.:-0.72367   1st Qu.:-0.7137   
##  Median :-0.2331   Median :-0.1261   Median :-0.07692   Median :-0.1019   
##  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.00000   Mean   : 0.0000   
##  3rd Qu.: 0.7062   3rd Qu.: 0.1946   3rd Qu.: 0.62862   3rd Qu.: 0.6746   
##  Max.   : 3.1604   Max.   :13.7533   Max.   :14.91577   Max.   : 7.0987   
##     density               pH             sulphates      
##  Min.   :-2.38090   Min.   :-3.10123   Min.   :-2.3651  
##  1st Qu.:-0.78919   1st Qu.:-0.65126   1st Qu.:-0.7002  
##  Median :-0.09519   Median :-0.05532   Median :-0.1745  
##  Mean   : 0.00000   Mean   : 0.00000   Mean   : 0.0000  
##  3rd Qu.: 0.72311   3rd Qu.: 0.60684   3rd Qu.: 0.5265  
##  Max.   : 2.90178   Max.   : 4.18247   Max.   : 5.1706  
##     alcohol        
##  Min.   :-2.04414  
##  1st Qu.:-0.82479  
##  Median :-0.09317  
##  Mean   : 0.00000  
##  3rd Qu.: 0.71973  
##  Max.   : 2.99587
describe(dados_normalizados)
##                    vars    n mean sd median trimmed  mad   min   max range
## quality               1 4891    0  1   0.14   -0.03 1.67 -3.25  3.52  6.77
## fixedacidity          2 4891    0  1  -0.06   -0.05 0.88 -3.62  8.70 12.32
## volatileacidity       3 4891    0  1  -0.18   -0.11 0.89 -1.97  8.19 10.17
## citricacid            4 4891    0  1  -0.12   -0.07 0.74 -2.76 10.96 13.72
## residualsugar         5 4891    0  1  -0.23   -0.11 1.08 -1.16  3.16  4.32
## chlorides             6 4891    0  1  -0.13   -0.13 0.48 -1.68 13.75 15.44
## freesulfurdioxide     7 4891    0  1  -0.08   -0.06 0.96 -1.96 14.92 16.87
## totalsulfurdioxide    8 4891    0  1  -0.10   -0.03 1.01 -3.04  7.10 10.14
## density               9 4891    0  1  -0.10   -0.03 1.09 -2.38  2.90  5.28
## pH                   10 4891    0  1  -0.06   -0.04 0.98 -3.10  4.18  7.28
## sulphates            11 4891    0  1  -0.17   -0.09 0.91 -2.37  5.17  7.54
## alcohol              12 4891    0  1  -0.09   -0.07 1.21 -2.04  3.00  5.04
##                    skew kurtosis   se
## quality            0.16     0.21 0.01
## fixedacidity       0.65     2.17 0.01
## volatileacidity    1.54     4.81 0.01
## citricacid         1.28     6.18 0.01
## residualsugar      0.73    -0.52 0.01
## chlorides          5.03    37.68 0.01
## freesulfurdioxide  1.41    11.46 0.01
## totalsulfurdioxide 0.39     0.57 0.01
## density            0.25    -0.76 0.01
## pH                 0.46     0.53 0.01
## sulphates          0.98     1.59 0.01
## alcohol            0.49    -0.70 0.01

Análise:

Criamos a base de dados “dados_normalizados” normalizando (subtraindo a média e dividindo pelo desvio padrão) para uso posterior

# componentes principais - básico
pca1 <- princomp(white1[complete.cases(white1),], cor=TRUE)
summary(pca1)
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     1.8376211 1.2601782 1.1725041 1.04144219 0.98963356
## Proportion of Variance 0.2814043 0.1323374 0.1145638 0.09038349 0.08161455
## Cumulative Proportion  0.2814043 0.4137417 0.5283055 0.61868901 0.70030356
##                            Comp.6     Comp.7     Comp.8     Comp.9
## Standard deviation     0.96393790 0.87026920 0.84619866 0.74637002
## Proportion of Variance 0.07743136 0.06311404 0.05967101 0.04642235
## Cumulative Proportion  0.77773492 0.84084896 0.90051997 0.94694232
##                          Comp.10    Comp.11     Comp.12
## Standard deviation     0.5812201 0.53360218 0.118928612
## Proportion of Variance 0.0281514 0.02372761 0.001178668
## Cumulative Proportion  0.9750937 0.99882133 1.000000000

Análise:

Avaiando proposção acumulada das componentes principais (28,14%, 41,37%, …) observamos que não houve grande ganho com relação as variáveis originais, como era esperado, já que não existem muita correlação entre as variáveis da nossa base

Vamos usar a metodologia de Compenetes Principais para algumas variáveis que apresentaram alguma correlação: residualsugar, density e alcohol. Para isso criaremos uma base de dados “white1pca” somente com estas variáveis

# componentes principais - Variáveias alta correlação

white1pca <- white1[,c(-1, -2, -3, -4, -6, -7, -8, -10, -11)]
pca2 <- princomp(white1pca[complete.cases(white1pca),], cor = TRUE)
summary(pca2)
## Importance of components:
##                          Comp.1    Comp.2     Comp.3
## Standard deviation     1.553126 0.7335335 0.22299680
## Proportion of Variance 0.804067 0.1793571 0.01657586
## Cumulative Proportion  0.804067 0.9834241 1.00000000
dados_normalizados1 <- as.data.frame(scale(white1pca))

Análise:

Como era esperado, o uso de PCA para as variáveis: residualsugar, density e alcohol apresentou bom resuldado já que estas tem alta correlação entre si. A proposção acumulada já é de 80,40% na primeria componete

library(psych)

# Escolher os componentes principais
fa.parallel (white1pca, fa="pc", show.legend=FALSE, main = "Eigenvalues dos componentes 
             principais")
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A loading greater than abs(1) was detected. Examine the loadings
## carefully.
## The estimated weights for the factor scores are probably incorrect.  Try a different factor extraction method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : An ultra-Heywood case was detected. Examine the results carefully

## Parallel analysis suggests that the number of factors =  NA  and the number of components =  1

Análise:

Como visto anteriormente, escolheremos a 1a compenente principal pois ele sozinha já explica/consolida grnade parte da informação das e variáveis

# Rotação varimax


library(psych)
# Varimax Rotated Principal Components
# # extrair os fatores
vinhospca  <- principal(white1pca, nfactors=1, scores=T, rotate="varimax")
vinhospca  # print results 
## Principal Components Analysis
## Call: principal(r = white1pca, nfactors = 1, rotate = "varimax", scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
##                 PC1   h2   u2 com
## residualsugar  0.86 0.73 0.27   1
## density        0.98 0.97 0.03   1
## alcohol       -0.84 0.71 0.29   1
## 
##                 PC1
## SS loadings    2.41
## Proportion Var 0.80
## 
## Mean item complexity =  1
## Test of the hypothesis that 1 component is sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.15 
##  with the empirical chi square  661.34  with prob <  NA 
## 
## Fit based upon off diagonal values = 0.96
fator01 = vinhospca$scores[,1]
hist(fator01)

white1<-cbind(white1,fator01)
#fix(matriz)

plot(quality,fator01)

matcor <- cor(white1)
print(matcor, digits = 2)
##                    quality fixedacidity volatileacidity citricacid
## quality             1.0000       -0.114         -0.1963    -0.0088
## fixedacidity       -0.1141        1.000         -0.0248     0.2895
## volatileacidity    -0.1963       -0.025          1.0000    -0.1529
## citricacid         -0.0088        0.290         -0.1529     1.0000
## residualsugar      -0.0995        0.087          0.0460     0.0914
## chlorides          -0.2095        0.023          0.0700     0.1132
## freesulfurdioxide   0.0088       -0.049         -0.0949     0.0943
## totalsulfurdioxide -0.1746        0.091          0.0892     0.1207
## density            -0.3176        0.268          0.0032     0.1483
## pH                  0.0991       -0.427         -0.0334    -0.1643
## sulphates           0.0535       -0.017         -0.0379     0.0616
## alcohol             0.4363       -0.120          0.0673    -0.0765
## fator01            -0.3174        0.182         -0.0058     0.1197
##                    residualsugar chlorides freesulfurdioxide
## quality                   -0.100    -0.210           0.00876
## fixedacidity               0.087     0.023          -0.04884
## volatileacidity            0.046     0.070          -0.09485
## citricacid                 0.091     0.113           0.09425
## residualsugar              1.000     0.086           0.30987
## chlorides                  0.086     1.000           0.10095
## freesulfurdioxide          0.310     0.101           1.00000
## totalsulfurdioxide         0.408     0.199           0.61591
## density                    0.831     0.261           0.30898
## pH                        -0.199    -0.091           0.00018
## sulphates                 -0.028     0.017           0.06009
## alcohol                   -0.462    -0.362          -0.25022
## fator01                    0.856     0.264           0.32348
##                    totalsulfurdioxide density       pH sulphates alcohol
## quality                       -0.1746 -0.3176  0.09913     0.053   0.436
## fixedacidity                   0.0905  0.2682 -0.42667    -0.017  -0.120
## volatileacidity                0.0892  0.0032 -0.03342    -0.038   0.067
## citricacid                     0.1207  0.1483 -0.16430     0.062  -0.077
## residualsugar                  0.4081  0.8315 -0.19916    -0.028  -0.462
## chlorides                      0.1990  0.2613 -0.09063     0.017  -0.362
## freesulfurdioxide              0.6159  0.3090  0.00018     0.060  -0.250
## totalsulfurdioxide             1.0000  0.5436  0.00274     0.135  -0.448
## density                        0.5436  1.0000 -0.09845     0.075  -0.806
## pH                             0.0027 -0.0984  1.00000     0.155   0.121
## sulphates                      0.1348  0.0748  0.15517     1.000  -0.018
## alcohol                       -0.4484 -0.8064  0.12103    -0.018   1.000
## fator01                        0.5233  0.9849 -0.15312     0.027  -0.843
##                    fator01
## quality            -0.3174
## fixedacidity        0.1823
## volatileacidity    -0.0058
## citricacid          0.1197
## residualsugar       0.8557
## chlorides           0.2636
## freesulfurdioxide   0.3235
## totalsulfurdioxide  0.5233
## density             0.9849
## pH                 -0.1531
## sulphates           0.0270
## alcohol            -0.8425
## fator01             1.0000
#attach(matriz)

#write.table(file='E:/LabBDT2018/Analise_vinhos.csv',matriz, sep=';',dec=',')

Análise:

Incluimos no banco de dados white1 uma coluna fator01 que é a combinação , via método PCA, das variáveis residualsugar, density e alcohol. O fator01 poderá substituir estas 3 variáveis em outros modelos com pequenas perdas, tendo um modelo redizido (menos variáveis).

Podemos verificar isso olhando as correlações: altas entre o fator01 e as 3 variáveis (residualsugar 85,57%, density 98,49% e alcohol -84,25%) e no mesmo paramar com a variável de resposta quality -31,74% que as outras 3

Partindo agora para os modelos de predição

Começamos com regressão linerar

attach(white1)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white1 (pos = 3):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 7):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 8):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 10):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
Modelo1 <- lm(quality ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)

summary(Modelo1)
## 
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + citricacid + 
##     residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide + 
##     density + pH + sulphates + alcohol)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8860 -0.4972 -0.0425  0.4624  3.1111 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         2.255e+02  2.336e+01   9.652  < 2e-16 ***
## fixedacidity        1.198e-01  2.319e-02   5.165 2.49e-07 ***
## volatileacidity    -1.880e+00  1.135e-01 -16.560  < 2e-16 ***
## citricacid          3.698e-02  9.552e-02   0.387 0.698666    
## residualsugar       1.061e-01  8.735e-03  12.148  < 2e-16 ***
## chlorides           7.384e-02  5.474e-01   0.135 0.892707    
## freesulfurdioxide   3.450e-03  8.435e-04   4.090 4.38e-05 ***
## totalsulfurdioxide  8.962e-05  3.837e-04   0.234 0.815337    
## density            -2.264e+02  2.367e+01  -9.566  < 2e-16 ***
## pH                  9.097e-01  1.130e-01   8.051 1.02e-15 ***
## sulphates           7.204e-01  1.015e-01   7.096 1.47e-12 ***
## alcohol             1.037e-01  2.958e-02   3.505 0.000461 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7489 on 4879 degrees of freedom
## Multiple R-squared:  0.2873, Adjusted R-squared:  0.2857 
## F-statistic: 178.8 on 11 and 4879 DF,  p-value: < 2.2e-16

Análise:

O modelo com todas as variáveis tem um R2 Ajustado de 28,57% e Residual Standard Error de 0,7489 Parametros para escolher o melhor modelo é um maior R2 ajustado e/ou um menor Residual Standard Error

Com temos alguma variáveis com alto p-Valor, valor tira-los do modelo (citricacid, chlorides, totalsulfurdioxide), abaixo

Modelo2 <- lm(quality ~ fixedacidity+volatileacidity+residualsugar+freesulfurdioxide+density+pH+sulphates+alcohol)

summary(Modelo2)
## 
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + residualsugar + 
##     freesulfurdioxide + density + pH + sulphates + alcohol)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8969 -0.4944 -0.0422  0.4617  3.1110 
## 
## Coefficients:
##                       Estimate   Std. Error t value Pr(>|t|)    
## (Intercept)        222.6060716   22.0610591  10.090  < 2e-16 ***
## fixedacidity         0.1193286    0.0225543   5.291 1.27e-07 ***
## volatileacidity     -1.8801511    0.1092153 -17.215  < 2e-16 ***
## residualsugar        0.1051611    0.0083239  12.634  < 2e-16 ***
## freesulfurdioxide    0.0035924    0.0006757   5.317 1.10e-07 ***
## density           -223.4943952   22.3350205 -10.006  < 2e-16 ***
## pH                   0.8998353    0.1100877   8.174 3.77e-16 ***
## sulphates            0.7219599    0.1012550   7.130 1.15e-12 ***
## alcohol              0.1059325    0.0291161   3.638 0.000277 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7487 on 4882 degrees of freedom
## Multiple R-squared:  0.2873, Adjusted R-squared:  0.2861 
## F-statistic:   246 on 8 and 4882 DF,  p-value: < 2.2e-16

Análise:

O modelo sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% (levemente melhor que o anterior) e Residual Standard Error de 0,7487 (leventente melhor que o anterior), mas com um modelo com menos variáveis

Agora vamos testar um modelo com o PCA trabalhado acima fator01, tirando as variáveis que o compoem (residualsugar, density e alcohol)

Modelo3 <- lm(quality ~ fixedacidity+volatileacidity+freesulfurdioxide+pH+sulphates+fator01)

summary(Modelo3)
## 
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + freesulfurdioxide + 
##     pH + sulphates + fator01)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.3985 -0.5299 -0.0473  0.5246  3.4903 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        6.0443781  0.3371370  17.929  < 2e-16 ***
## fixedacidity      -0.0473671  0.0155284  -3.050 0.002298 ** 
## volatileacidity   -1.6608174  0.1170109 -14.194  < 2e-16 ***
## freesulfurdioxide  0.0050022  0.0007339   6.816 1.05e-11 ***
## pH                 0.0833160  0.0869460   0.958 0.337984    
## sulphates          0.3631688  0.1038230   3.498 0.000473 ***
## fator01           -0.3016249  0.0126504 -23.843  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8151 on 4884 degrees of freedom
## Multiple R-squared:  0.1548, Adjusted R-squared:  0.1538 
## F-statistic: 149.1 on 6 and 4884 DF,  p-value: < 2.2e-16

Análise:

O modelo com PCA tem um R2 Ajustado de 15,38% (pior que o anterior) e Residual Standard Error de 0,8151 (pior que o anterior), mas com um modelo com menos variáveis. Não avaliamos como boa este modelo.

Agora vamos testar um modelo com o PCA trabalhado acima fator01, tirando as variáveis que o compoem (residualsugar, density e alcohol) e também as não significativas no modelo acima (pH)

Modelo4 <- lm(quality ~ fixedacidity+volatileacidity+freesulfurdioxide+sulphates+fator01)

summary(Modelo4)
## 
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + freesulfurdioxide + 
##     sulphates + fator01)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.3839 -0.5296 -0.0442  0.5216  3.5062 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        6.3454655  0.1222127  51.921  < 2e-16 ***
## fixedacidity      -0.0534901  0.0141526  -3.780 0.000159 ***
## volatileacidity   -1.6657118  0.1168984 -14.249  < 2e-16 ***
## freesulfurdioxide  0.0049974  0.0007338   6.810 1.09e-11 ***
## sulphates          0.3796090  0.1023948   3.707 0.000212 ***
## fator01           -0.3026365  0.0126061 -24.007  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8151 on 4885 degrees of freedom
## Multiple R-squared:  0.1547, Adjusted R-squared:  0.1538 
## F-statistic: 178.8 on 5 and 4885 DF,  p-value: < 2.2e-16

Análise:

O modelo com PCA e sem pH tem um R2 Ajustado de 15,38% (igual o anterior) e Residual Standard Error de 0,8151 (igual o anterior), mas com um modelo com menos variáveis. Não avaliamos como boa este modelo e descartaremos o uso de PCA nesta regressão

Sendo assim, avaliamos que o melhor modelo é o 2: Sem PCA e com somente as varíaveis que foram significativas. O modelo sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% e Residual Standard Error de 0,7487, mas com um modelo com menos variáveis

Vamos agora avaliar como o método Stepwise escolheria quais as variáveis que este modelo de previsão, iniciando com todos as variáveis

step(Modelo1)
## Start:  AIC=-2816.85
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar + 
##     chlorides + freesulfurdioxide + totalsulfurdioxide + density + 
##     pH + sulphates + alcohol
## 
##                      Df Sum of Sq    RSS     AIC
## - chlorides           1     0.010 2736.2 -2818.8
## - totalsulfurdioxide  1     0.031 2736.2 -2818.8
## - citricacid          1     0.084 2736.3 -2818.7
## <none>                            2736.2 -2816.8
## - alcohol             1     6.888 2743.1 -2806.6
## - freesulfurdioxide   1     9.382 2745.6 -2802.1
## - fixedacidity        1    14.964 2751.2 -2792.2
## - sulphates           1    28.238 2764.4 -2768.6
## - pH                  1    36.353 2772.5 -2754.3
## - density             1    51.317 2787.5 -2728.0
## - residualsugar       1    82.755 2818.9 -2673.1
## - volatileacidity     1   153.788 2890.0 -2551.4
## 
## Step:  AIC=-2818.83
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar + 
##     freesulfurdioxide + totalsulfurdioxide + density + pH + sulphates + 
##     alcohol
## 
##                      Df Sum of Sq    RSS     AIC
## - totalsulfurdioxide  1     0.030 2736.2 -2820.8
## - citricacid          1     0.091 2736.3 -2820.7
## <none>                            2736.2 -2818.8
## - alcohol             1     6.912 2743.1 -2808.5
## - freesulfurdioxide   1     9.413 2745.6 -2804.0
## - fixedacidity        1    15.336 2751.5 -2793.5
## - sulphates           1    28.251 2764.4 -2770.6
## - pH                  1    37.318 2773.5 -2754.6
## - density             1    52.642 2788.8 -2727.6
## - residualsugar       1    86.021 2822.2 -2669.4
## - volatileacidity     1   155.126 2891.3 -2551.1
## 
## Step:  AIC=-2820.77
## quality ~ fixedacidity + volatileacidity + citricacid + residualsugar + 
##     freesulfurdioxide + density + pH + sulphates + alcohol
## 
##                     Df Sum of Sq    RSS     AIC
## - citricacid         1     0.095 2736.3 -2822.6
## <none>                           2736.2 -2820.8
## - alcohol            1     7.186 2743.4 -2809.9
## - fixedacidity       1    15.389 2751.6 -2795.3
## - freesulfurdioxide  1    15.558 2751.8 -2795.0
## - sulphates          1    28.355 2764.6 -2772.3
## - pH                 1    37.417 2773.6 -2756.3
## - density            1    56.027 2792.2 -2723.6
## - residualsugar      1    89.342 2825.6 -2665.6
## - volatileacidity    1   160.569 2896.8 -2543.9
## 
## Step:  AIC=-2822.6
## quality ~ fixedacidity + volatileacidity + residualsugar + freesulfurdioxide + 
##     density + pH + sulphates + alcohol
## 
##                     Df Sum of Sq    RSS     AIC
## <none>                           2736.3 -2822.6
## - alcohol            1     7.419 2743.7 -2811.4
## - fixedacidity       1    15.689 2752.0 -2796.6
## - freesulfurdioxide  1    15.844 2752.2 -2796.4
## - sulphates          1    28.495 2764.8 -2773.9
## - pH                 1    37.447 2773.8 -2758.1
## - density            1    56.122 2792.4 -2725.3
## - residualsugar      1    89.459 2825.8 -2667.3
## - volatileacidity    1   166.107 2902.4 -2536.4
## 
## Call:
## lm(formula = quality ~ fixedacidity + volatileacidity + residualsugar + 
##     freesulfurdioxide + density + pH + sulphates + alcohol)
## 
## Coefficients:
##       (Intercept)       fixedacidity    volatileacidity  
##        222.606072           0.119329          -1.880151  
##     residualsugar  freesulfurdioxide            density  
##          0.105161           0.003592        -223.494395  
##                pH          sulphates            alcohol  
##          0.899835           0.721960           0.105932

Análise:

A conclusão é a mesma do Modelo2. O que confirma o que fizemos até agora.

O modelo sem PCA e sem as variáveis não siginificativas tem um R2 Ajustado de 28,61% (levemente melhor que o anterior) e Residual Standard Error de 0,7487 (leventente melhor que o anterior), mas com um modelo com menos variáveis

Vamos agora analisar os resíduos: contra os valores ajustados, sua normalidade e aleatoriedade

library(lmtest)
## Warning: package 'lmtest' was built under R version 3.4.4
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.4.4
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
plot(Modelo2, which = 1)

plot(Modelo2, which = 2)

dwtest (Modelo2$residuals ~ Modelo2$fitted.values)
## 
##  Durbin-Watson test
## 
## data:  Modelo2$residuals ~ Modelo2$fitted.values
## DW = 1.9562, p-value = 0.06256
## alternative hypothesis: true autocorrelation is greater than 0

Análise:

Temos alguns pontos (resíduos) um pouco grandes (> 3) para valores ajustados maiores (>6), que também aparecem nas caudas do gráfico de probabilidade Normal. O teste de DW para aleatoriedade tem P-valor um pouco acima de 5% (6,2%)

Com isso ficaremos com este modelo, com atenção ao comportamento de previsão para notas de qualidade >6

Vamos agora para análises pela árvore de regressão

## Árvore de Regressão


attach(white1)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white1 (pos = 5):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 9):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 10):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 11):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 13):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
#install.packages("rpart")
#install.packages("rpart.plot")
library(rpart)
library(rpart.plot)
## Warning: package 'rpart.plot' was built under R version 3.4.4
modelo_Valor_tree <- rpart (quality ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, cp = 0.001,minsplit = 5,maxdepth=10)


# Faz o Gráfico
rpart.plot(modelo_Valor_tree, type=0, extra="auto", under=TRUE, clip.right.labs=TRUE,
           fallen.leaves=FALSE,   digits=2, varlen=-10, faclen=20,
           cex=0.4, tweak=1.7,
           compress=TRUE,
           snip=FALSE)
## Warning: labs do not fit even at cex 0.15, there may be some overplotting
## Warning: cex and tweak both specified, applying both

Val_pred_tree <- predict(modelo_Valor_tree,interval = "prediction", level = 0.95) 
str(Val_pred_tree)
##  Named num [1:4891] 5.72 6.41 5.88 5.31 6.39 ...
##  - attr(*, "names")= chr [1:4891] "1" "2" "3" "4" ...
mse_tree <- mean((quality - Val_pred_tree)^2)
sqrt(mse_tree)
## [1] 0.5914769
# grafico residuo
rs <- Val_pred_tree- quality
plot(predict(modelo_Valor_tree), rs, xlab = "Com Árvore de Regressão",ylab = "Residuos")
abline(h = 0, lty = 2)

qqnorm(rs)
qqline(rs)

dwtest (rs ~ Val_pred_tree)
## 
##  Durbin-Watson test
## 
## data:  rs ~ Val_pred_tree
## DW = 1.9183, p-value = 0.002123
## alternative hypothesis: true autocorrelation is greater than 0

Análise:

A Arvore de Regressão Residual Standard Error de 0,5914 (melhor que o melhor modelo de Regressão linear 0,7487)

Analisando os resíduos, não vemos valores maiores do que 3 desvios padrão, nem abaixo nem acima. Olhand o gráfico de probabilidade Normal, a distribuição parece normal O teste de DW para aleatoriedade tem P-valor de 0,2%. Então podemos assumir a aleatoriedade dos resíduos

Com isso podemos concluir que a Arvore de Regressão apresenta resultados melhores do que a Regressão linear para prever a quality dos vinhos brancos, com base nos dads que temos

Para tentar melhor nossa previsão, vamos transformar a variável de resposta “quality” em uma variável discreta. A variável será “Bom_ruim”, onde 0 será para vinhos ruins (quality = 3, 4, 5) e 1 será para vinhos bons (quality = 7, 8, 9)

Criaremos um novo banco de dados chamado white2 onde só teremos os vinhos com quality diferente de 6

white1[,"Bom_ruim"] <- ifelse(white1$quality == 3, 0, ifelse(white1$quality == 4, 0, ifelse(white1$quality == 5, 0, ifelse(white1$quality == 7, 1, ifelse(white1$quality == 8, 1, ifelse(white1$quality == 9, 1, 6))))))


white2 <- subset(white1, white1$Bom_ruim != 6)
summary(white2)
##     quality       fixedacidity    volatileacidity    citricacid   
##  Min.   :3.000   Min.   : 3.900   Min.   :0.0800   Min.   :0.000  
##  1st Qu.:5.000   1st Qu.: 6.300   1st Qu.:0.2200   1st Qu.:0.260  
##  Median :5.000   Median : 6.800   Median :0.2800   Median :0.310  
##  Mean   :5.779   Mean   : 6.869   Mean   :0.2927   Mean   :0.331  
##  3rd Qu.:7.000   3rd Qu.: 7.400   3rd Qu.:0.3400   3rd Qu.:0.390  
##  Max.   :9.000   Max.   :11.800   Max.   :1.1000   Max.   :1.000  
##  residualsugar      chlorides       freesulfurdioxide totalsulfurdioxide
##  Min.   : 0.600   Min.   :0.00900   Min.   :  2.00    Min.   :  9.0     
##  1st Qu.: 1.700   1st Qu.:0.03600   1st Qu.: 22.00    1st Qu.:109.0     
##  Median : 5.100   Median :0.04300   Median : 34.00    Median :135.5     
##  Mean   : 6.338   Mean   :0.04619   Mean   : 35.01    Mean   :139.4     
##  3rd Qu.: 9.800   3rd Qu.:0.05100   3rd Qu.: 46.00    3rd Qu.:169.0     
##  Max.   :22.000   Max.   :0.34600   Max.   :289.00    Max.   :440.0     
##     density             pH          sulphates         alcohol     
##  Min.   :0.9871   Min.   :2.790   Min.   :0.2200   Min.   : 8.00  
##  1st Qu.:0.9918   1st Qu.:3.090   1st Qu.:0.4100   1st Qu.: 9.40  
##  Median :0.9938   Median :3.170   Median :0.4700   Median :10.20  
##  Mean   :0.9941   Mean   :3.188   Mean   :0.4889   Mean   :10.46  
##  3rd Qu.:0.9963   3rd Qu.:3.280   3rd Qu.:0.5400   3rd Qu.:11.40  
##  Max.   :1.0024   Max.   :3.820   Max.   :1.0800   Max.   :14.20  
##     fator01            Bom_ruim     
##  Min.   :-2.32828   Min.   :0.0000  
##  1st Qu.:-0.79655   1st Qu.:0.0000  
##  Median :-0.08207   Median :0.0000  
##  Mean   : 0.02321   Mean   :0.3929  
##  3rd Qu.: 0.80761   3rd Qu.:1.0000  
##  Max.   : 2.68198   Max.   :1.0000
attach(white2)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white1 (pos = 5):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 8):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 9):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 12):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 13):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 14):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 16):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
par (mfrow=c(3,4))
plot (fixedacidity, Bom_ruim)
plot (volatileacidity, Bom_ruim)
plot (citricacid, Bom_ruim)
plot (residualsugar, Bom_ruim)
plot (chlorides, Bom_ruim)
plot (freesulfurdioxide, Bom_ruim)
plot (totalsulfurdioxide, Bom_ruim)
plot (density, Bom_ruim)
plot (pH, Bom_ruim)
plot (sulphates, Bom_ruim)
plot (alcohol, Bom_ruim)

attach(white2)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white2 (pos = 3):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 6):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 9):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 10):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 13):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 14):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 15):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 17):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
Modelo_RegLog0 <- glm(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, family=binomial(link="logit"))

summary(Modelo_RegLog0)
## 
## Call:
## glm(formula = Bom_ruim ~ fixedacidity + volatileacidity + citricacid + 
##     residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide + 
##     density + pH + sulphates + alcohol, family = binomial(link = "logit"))
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.8455  -0.5814  -0.2156   0.5788   2.9851  
## 
## Coefficients:
##                       Estimate  Std. Error z value Pr(>|z|)    
## (Intercept)         887.802478  126.549694   7.015 2.29e-12 ***
## fixedacidity          0.635214    0.126503   5.021 5.13e-07 ***
## volatileacidity      -9.767008    0.745034 -13.109  < 2e-16 ***
## citricacid           -0.830594    0.571996  -1.452 0.146474    
## residualsugar         0.443592    0.047983   9.245  < 2e-16 ***
## chlorides            -8.220289    5.131638  -1.602 0.109181    
## freesulfurdioxide     0.005858    0.004341   1.350 0.177157    
## totalsulfurdioxide    0.002249    0.002107   1.067 0.285856    
## density            -917.348855  128.353867  -7.147 8.87e-13 ***
## pH                    3.646380    0.591466   6.165 7.05e-10 ***
## sulphates             3.337707    0.521060   6.406 1.50e-10 ***
## alcohol               0.559339    0.157586   3.549 0.000386 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 3615.4  on 2697  degrees of freedom
## Residual deviance: 2116.1  on 2686  degrees of freedom
## AIC: 2140.1
## 
## Number of Fisher Scoring iterations: 6
table(white2$Bom_ruim, predict(Modelo_RegLog0) > 0.5)
##    
##     FALSE TRUE
##   0  1496  142
##   1   359  701
attach(white2)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white2 (pos = 3):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 4):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 7):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 10):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 11):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 14):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 15):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 16):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 18):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
Modelo_RegLog1 <- glm(Bom_ruim ~ fixedacidity+volatileacidity+residualsugar+density+pH+sulphates+alcohol, family=binomial(link="logit"))

summary(Modelo_RegLog1)
## 
## Call:
## glm(formula = Bom_ruim ~ fixedacidity + volatileacidity + residualsugar + 
##     density + pH + sulphates + alcohol, family = binomial(link = "logit"))
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.9386  -0.5828  -0.2359   0.5809   2.9527  
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      899.2217   118.0834   7.615 2.63e-14 ***
## fixedacidity       0.6073     0.1210   5.017 5.24e-07 ***
## volatileacidity   -9.5085     0.7074 -13.441  < 2e-16 ***
## residualsugar      0.4563     0.0455  10.030  < 2e-16 ***
## density         -929.2993   119.6595  -7.766 8.09e-15 ***
## pH                 3.7993     0.5766   6.589 4.44e-11 ***
## sulphates          3.4366     0.5163   6.656 2.82e-11 ***
## alcohol            0.5451     0.1543   3.532 0.000412 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 3615.4  on 2697  degrees of freedom
## Residual deviance: 2128.6  on 2690  degrees of freedom
## AIC: 2144.6
## 
## Number of Fisher Scoring iterations: 5
ICbeta1=confint.default(Modelo_RegLog1,level=0.95)
ICbeta1
##                         2.5 %       97.5 %
## (Intercept)       667.7824723 1130.6609856
## fixedacidity        0.3700683    0.8445550
## volatileacidity   -10.8950057   -8.1219758
## residualsugar       0.3671776    0.5455262
## density         -1163.8275122 -694.7709925
## pH                  2.6691027    4.9295041
## sulphates           2.4245760    4.4485818
## alcohol             0.2426526    0.8475608
table(white2$Bom_ruim, predict(Modelo_RegLog1) > 0.5)
##    
##     FALSE TRUE
##   0  1496  142
##   1   355  705
OR1=exp(Modelo_RegLog1$coefficients)
ICOR1=exp(ICbeta1)

round((cbind(OR1, ICOR1)),3)
##                    OR1         2.5 %  97.5 %
## (Intercept)        Inf 1.033339e+290     Inf
## fixedacidity     1.835  1.448000e+00   2.327
## volatileacidity  0.000  0.000000e+00   0.000
## residualsugar    1.578  1.444000e+00   1.726
## density          0.000  0.000000e+00   0.000
## pH              44.670  1.442700e+01 138.311
## sulphates       31.080  1.129700e+01  85.506
## alcohol          1.725  1.275000e+00   2.334

OR1 2.5 % 97.5 %

(Intercept) 0.053 0.002 1.618

idade 1.142 1.033 1.263

renda 0.042 0.002 0.726

Interpretação das razões de chance (odds ratio)

Tanto a idade quanto a renda familiar per capita estão significativamente relacionadas com a chance de autoavaliação de saúde não boa (OBS: Note que o p-valor é menor que o nível de significância de 5% e o IC para OR não inclui a unidade).

A chance do indivíduo reportar um estado de saúde não bom aumenta em 14,2% ao aumentar em 1 ano a idade.

Indivíduos com mais de 3 salários mínimos tem uma chance de reportar um estado de saúde não bom 95,8% menor do que os indivíduos que ganham no máximo 3 salários mínimos.

attach(white2)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white2 (pos = 3):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 4):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 5):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 8):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 11):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 12):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 15):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 16):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 17):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 19):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
Arvore_decisao1 <- rpart(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)

plot(Arvore_decisao1)
text(Arvore_decisao1, pretty = 0, cex = 0.6)

summary(Arvore_decisao1)
## Call:
## rpart(formula = Bom_ruim ~ fixedacidity + volatileacidity + citricacid + 
##     residualsugar + chlorides + freesulfurdioxide + totalsulfurdioxide + 
##     density + pH + sulphates + alcohol)
##   n= 2698 
## 
##           CP nsplit rel error    xerror        xstd
## 1 0.33749371      0 1.0000000 1.0003746 0.008449526
## 2 0.07431228      1 0.6625063 0.6631321 0.019390587
## 3 0.03745862      2 0.5881940 0.5899085 0.018425056
## 4 0.01959342      3 0.5507354 0.5528783 0.018833094
## 5 0.01843187      4 0.5311420 0.5424329 0.018808386
## 6 0.01412535      5 0.5127101 0.5243125 0.018655754
## 7 0.01368686      6 0.4985848 0.5220435 0.018485267
## 8 0.01000000      7 0.4848979 0.5152687 0.018312414
## 
## Variable importance
##            alcohol            density          chlorides 
##                 37                 24                 13 
##    volatileacidity totalsulfurdioxide  freesulfurdioxide 
##                  8                  6                  4 
##      residualsugar                 pH          sulphates 
##                  4                  2                  1 
## 
## Node number 1: 2698 observations,    complexity param=0.3374937
##   mean=0.3928836, MSE=0.2385261 
##   left son=2 (1731 obs) right son=3 (967 obs)
##   Primary splits:
##       alcohol            < 10.85    to the left,  improve=0.33749370, (0 missing)
##       density            < 0.99203  to the right, improve=0.23249920, (0 missing)
##       chlorides          < 0.0395   to the right, improve=0.16868680, (0 missing)
##       totalsulfurdioxide < 158.5    to the right, improve=0.09100253, (0 missing)
##       volatileacidity    < 0.2275   to the right, improve=0.05403458, (0 missing)
##   Surrogate splits:
##       density            < 0.991935 to the right, agree=0.878, adj=0.661, (0 split)
##       chlorides          < 0.0385   to the right, agree=0.776, adj=0.375, (0 split)
##       totalsulfurdioxide < 123.5    to the right, agree=0.702, adj=0.169, (0 split)
##       residualsugar      < 5.05     to the right, agree=0.658, adj=0.047, (0 split)
##       sulphates          < 0.335    to the right, agree=0.656, adj=0.041, (0 split)
## 
## Node number 2: 1731 observations,    complexity param=0.07431228
##   mean=0.1808203, MSE=0.1481243 
##   left son=4 (1400 obs) right son=5 (331 obs)
##   Primary splits:
##       volatileacidity < 0.205    to the right, improve=0.18651550, (0 missing)
##       alcohol         < 10.11667 to the left,  improve=0.05776711, (0 missing)
##       pH              < 3.315    to the left,  improve=0.04131870, (0 missing)
##       citricacid      < 0.265    to the left,  improve=0.03969394, (0 missing)
##       chlorides       < 0.0395   to the right, improve=0.02366558, (0 missing)
##   Surrogate splits:
##       pH                 < 2.915    to the right, agree=0.812, adj=0.015, (0 split)
##       sulphates          < 0.915    to the left,  agree=0.812, adj=0.015, (0 split)
##       totalsulfurdioxide < 24.5     to the right, agree=0.811, adj=0.009, (0 split)
##       density            < 0.990125 to the right, agree=0.810, adj=0.006, (0 split)
## 
## Node number 3: 967 observations,    complexity param=0.03745862
##   mean=0.7724922, MSE=0.175748 
##   left son=6 (69 obs) right son=7 (898 obs)
##   Primary splits:
##       freesulfurdioxide  < 11.5     to the left,  improve=0.14184460, (0 missing)
##       alcohol            < 11.725   to the left,  improve=0.10565340, (0 missing)
##       fixedacidity       < 7.35     to the right, improve=0.06552326, (0 missing)
##       totalsulfurdioxide < 77.5     to the left,  improve=0.05019448, (0 missing)
##       residualsugar      < 1.275    to the left,  improve=0.04827922, (0 missing)
##   Surrogate splits:
##       totalsulfurdioxide < 55.5     to the left,  agree=0.939, adj=0.145, (0 split)
## 
## Node number 4: 1400 observations,    complexity param=0.01412535
##   mean=0.1, MSE=0.09 
##   left son=8 (1224 obs) right son=9 (176 obs)
##   Primary splits:
##       pH              < 3.325    to the left,  improve=0.07214506, (0 missing)
##       volatileacidity < 0.2825   to the right, improve=0.06355938, (0 missing)
##       alcohol         < 10.25    to the left,  improve=0.06301544, (0 missing)
##       chlorides       < 0.0445   to the right, improve=0.03032236, (0 missing)
##       density         < 0.993045 to the right, improve=0.02270628, (0 missing)
##   Surrogate splits:
##       fixedacidity      < 5.45     to the right, agree=0.879, adj=0.034, (0 split)
##       freesulfurdioxide < 114.25   to the left,  agree=0.876, adj=0.011, (0 split)
## 
## Node number 5: 331 observations,    complexity param=0.01843187
##   mean=0.5226586, MSE=0.2494866 
##   left son=10 (252 obs) right son=11 (79 obs)
##   Primary splits:
##       residualsugar     < 12.3     to the left,  improve=0.14363890, (0 missing)
##       density           < 0.99674  to the left,  improve=0.13288490, (0 missing)
##       alcohol           < 9.15     to the right, improve=0.08314618, (0 missing)
##       freesulfurdioxide < 24.5     to the left,  improve=0.08103964, (0 missing)
##       citricacid        < 0.235    to the left,  improve=0.05392591, (0 missing)
##   Surrogate splits:
##       density            < 0.99674  to the left,  agree=0.970, adj=0.873, (0 split)
##       alcohol            < 9.15     to the right, agree=0.900, adj=0.582, (0 split)
##       pH                 < 2.965    to the right, agree=0.813, adj=0.215, (0 split)
##       chlorides          < 0.0555   to the left,  agree=0.785, adj=0.101, (0 split)
##       totalsulfurdioxide < 207      to the left,  agree=0.779, adj=0.076, (0 split)
## 
## Node number 6: 69 observations
##   mean=0.2028986, MSE=0.1617307 
## 
## Node number 7: 898 observations,    complexity param=0.01959342
##   mean=0.8162584, MSE=0.1499807 
##   left son=14 (393 obs) right son=15 (505 obs)
##   Primary splits:
##       alcohol       < 11.725   to the left,  improve=0.09362169, (0 missing)
##       fixedacidity  < 7.35     to the right, improve=0.06222361, (0 missing)
##       density       < 0.991655 to the right, improve=0.04346013, (0 missing)
##       residualsugar < 0.975    to the left,  improve=0.04297555, (0 missing)
##       chlorides     < 0.0395   to the right, improve=0.04144398, (0 missing)
##   Surrogate splits:
##       density            < 0.991115 to the right, agree=0.720, adj=0.361, (0 split)
##       volatileacidity    < 0.2675   to the left,  agree=0.670, adj=0.247, (0 split)
##       chlorides          < 0.0385   to the right, agree=0.651, adj=0.204, (0 split)
##       residualsugar      < 1.475    to the left,  agree=0.624, adj=0.140, (0 split)
##       totalsulfurdioxide < 142.5    to the right, agree=0.602, adj=0.092, (0 split)
## 
## Node number 8: 1224 observations
##   mean=0.06944444, MSE=0.06462191 
## 
## Node number 9: 176 observations,    complexity param=0.01368686
##   mean=0.3125, MSE=0.2148438 
##   left son=18 (136 obs) right son=19 (40 obs)
##   Primary splits:
##       alcohol            < 10.48333 to the left,  improve=0.2329412, (0 missing)
##       density            < 0.9939   to the right, improve=0.2082860, (0 missing)
##       volatileacidity    < 0.2975   to the right, improve=0.1321515, (0 missing)
##       chlorides          < 0.0445   to the right, improve=0.1186099, (0 missing)
##       totalsulfurdioxide < 160.5    to the right, improve=0.1121008, (0 missing)
##   Surrogate splits:
##       density           < 0.992995 to the right, agree=0.812, adj=0.175, (0 split)
##       citricacid        < 0.58     to the left,  agree=0.784, adj=0.050, (0 split)
##       freesulfurdioxide < 7.5      to the right, agree=0.784, adj=0.050, (0 split)
## 
## Node number 10: 252 observations
##   mean=0.4166667, MSE=0.2430556 
## 
## Node number 11: 79 observations
##   mean=0.8607595, MSE=0.1198526 
## 
## Node number 14: 393 observations
##   mean=0.6819338, MSE=0.2169001 
## 
## Node number 15: 505 observations
##   mean=0.9207921, MSE=0.07293403 
## 
## Node number 18: 136 observations
##   mean=0.1911765, MSE=0.154628 
## 
## Node number 19: 40 observations
##   mean=0.725, MSE=0.199375
table(white2$Bom_ruim, predict(Arvore_decisao1) > 0.5)
##    
##     FALSE TRUE
##   0  1451  187
##   1   230  830
attach(white2)
## The following object is masked _by_ .GlobalEnv:
## 
##     fator01
## The following objects are masked from white2 (pos = 3):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 4):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 5):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white2 (pos = 6):
## 
##     alcohol, Bom_ruim, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 9):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 12):
## 
##     alcohol, chlorides, citricacid, density, fator01,
##     fixedacidity, freesulfurdioxide, pH, quality, residualsugar,
##     sulphates, totalsulfurdioxide, volatileacidity
## The following objects are masked from white1 (pos = 13):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from white:
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 16):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 17):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 18):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
## The following objects are masked from Vinhos (pos = 20):
## 
##     alcohol, chlorides, citricacid, density, fixedacidity,
##     freesulfurdioxide, pH, quality, residualsugar, sulphates,
##     totalsulfurdioxide, volatileacidity
#Rand_F <- randomForest(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol)



#Rand_Fom_forest.p <- classCenter(Bom_ruim ~ fixedacidity+volatileacidity+citricacid+residualsugar+chlorides+freesulfurdioxide+totalsulfurdioxide+density+pH+sulphates+alcohol, iris.rf$prox)
#plot(iris[,3], iris[,4], pch=21, xlab=names(iris)[3], ylab=names(iris)[4],
#bg=c("red", "blue", "green")[as.numeric(factor(iris$Species))],
#main="Iris Data with Prototypes")
#points(iris.p[,3], iris.p[,4], pch=21, cex=2, bg=c("red", "blue", "green"))